Chapter 9.2, Problem 25E

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6th Edition

Daniel C. Alexander + 1 other

ISBN: 9781285195698

Textbook Problem

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For the regular square pyramid shown in Exercise 24, suppose that the sides of the square base measure

a) Find the lateral area

b) Find the total area *T* of the pyramid.

c) Find the volume

To determine

**(a)**

**To find:**

The lateral area of the pyramid.

Explanation

**Given:**

A regular square pyramid shown, suppose that the sides of the square base measure

**Properties used:**

A pyramid is made by connecting a base to an apex. The base is flat with straight edges, no curves, hence, a polygon and all other faces are triangles.

A regular pyramid is a pyramid whose base is a regular polygon and whose lateral edges are all congruent.

The lateral area

In a regular pyramid, the lengths of the apothem

The perimeter of the square is four times the side.

**Calculation:**

From the given figure,

The sides of the square base measure

Since, the apothem is half the base length. Hence,

To determine

**(b)**

**To find:**

The total area of the pyramid.

To determine

**(c)**

**To find:**

The volume of the pyramid.

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